Statistical mechanics of an elastically pinned membrane: Equilibrium dynamics and power spectrum

TL;DR

This paper analytically models the dynamics of an elastically pinned membrane, deriving the power spectral density and demonstrating how membrane fluctuations can reveal the elasticity of cellular attachments.

Contribution

It provides an analytical calculation of the Green's function and power spectrum for a pinned membrane, enabling extraction of pinning elasticity from experimental data.

Findings

Analytical Green's function for pinned membrane dynamics.

Derived power spectral density considering experimental resolution.

Elasticity of membrane pinning can be inferred from fluctuation spectra.

Abstract

In biological settings membranes typically interact locally with other membranes or the extracellular matrix in the exterior, as well as with internal cellular structures such as the cytoskeleton. Characterization of the dynamic properties of such interactions presents a difficult task. Significant progress has been achieved through simulations and experiments, yet analytical progress in modelling pinned membranes has been impeded by the complexity of governing equations. Here we circumvent these difficulties by calculating analytically the time-dependent Green's function of the operator governing the dynamics of an elastically pinned membrane in a hydrodynamic surrounding and subject to external forces. This enables us to calculate the equilibrium power spectral density for an overdamped membrane pinned by an elastic, permanently-attached spring subject to thermal excitations. By considering the effects of the finite experimental resolution on the measured spectra, we show that the elasticity of the pinning can be extracted from the experimentally measured spectrum. Membrane fluctuations can thus be used as a tool to probe mechanical properties of the underlying structures. Such a tool may be particularly relevant in the context of cell mechanics, where the elasticity of the membrane's attachment to the cytoskeleton could be measured.